John Walker & Lydia Sawyer

I am looking for help. I know that my great, great, great grandfather was John Walker and I also know that he married Lydia Sawyer. I know that John was born in 1771 in England and came to the US in 1792. He died in Athens County Ohio in 1851 and I know for a while at least he lived in Hocking County. My problem is I have been unable to find anything that points to his parents. I have located many John Walkers that where born in England in 1771, but so far have been unable to trace tham to the US. I have even tried seaching out John Walkers born in the US at that time but none are the one I am looking for. If anyone has any information about this John Walker (he had children one of which was Nathaniel Seldon Walker) or any other suggestions as to where I might turn, please let me know. Thanks.